It looks like the CDC uses the 5 digit FIPS coding system, where the first two digits are the state FIPS codes and the last three digits correspond to the county FIPS codes.

Using IPUMS USA data, as you noted, you will need to combine STATEFIP with COUNTYFIPS to merge the two. Alternatively, you could split the CDC FIPS variable into two variables. Either method can be done in a statistical tool. For example, using Stata, the following would produce a combined STATEFIP/COUNTYFIPS variable: